Final answer:
In one-way ANOVA, the averaged and compared variable is the numerical response variable across different levels of a single categorical factor. The F statistic is used to determine significant differences between the group means.
Step-by-step explanation:
In a one-way ANOVA test, the variable that will be averaged and compared is the response variable. This test is designed to determine if there is a statistically significant difference between the means of three or more independent groups. The response variable is numerical and is measured across different levels of a single categorical factor. The null hypothesis tested by an ANOVA is that all group means are equal versus the alternative hypothesis that at least one group mean is different.
To perform the test, the ratio of the variance between group means to the variance within the groups, known as the F statistic, is calculated. The F statistic follows an F distribution, which has two types of degrees of freedom: one for the numerator (number of groups - 1) and one for the denominator (number of observations - number of groups).